用旅行商算法制作艺术图像

Making art with the Travelling Salesman Problem

Posted on 20th July by Mr Reid

The Travelling Salesman Problem is a classic problem in math­em­atics. The objective of the problem is to find the shortest pos­sible route between a number of cities that visits each city only once and returns to the starting point.

Below is a ren­dering of the text “MrReid.org” created by solving the Travelling Salesman Problem. If you look care­fully you can see that in each case the text is com­posed of one single line, drawn “without lifting the pen from the page”.

Top to bottom: “MrReid.org” rendered using 1000, 2000, and 5000 nodes. Click to enlarge.

By taking a grey­scale image, and turning it into a weighted Voronoi diagram (using Adrian Secord’s algorithm) it is pos­sible to create a “map” in which the “cities” are placed closer together in dark areas and further apart in light ones.

Top: the ori­ginal panda image. Bottom: weighted Voronoi diagram of panda image (10000 nodes).

By solving the Travelling Salesman Problem for this “map” (using the Nearest Neighbour algorithm for the first pass and and the 2-opt algorithm for sub­sequent optim­isa­tion) the fol­lowing “route” is produced.

There isn’t really enough con­trast between the back­ground and fore­ground in the ori­ginal panda image, but it works if you squint a little bit.

Tweet

This entry was posted in General and tagged art, mathematics. Bookmark the permalink.

← The Drinking Bird

Collision v allision →

 

 

参考代码下载： http://mrl.nyu.edu/~ajsecord/stipples.html

来源： http://wordpress.mrreid.org/2012/07/20/making-art-with-the-travelling-salesman-problem/